Detectives say the two are 33-year-old Joshua J. Tillery, who also goes by the name "Danger," and 22-year-old Tara L. Rader.
Spokane Police are also trying to find a 2006 black Pontiac Grand Prix, with Washington license plate AJR3220.
Anyone with information on these individuals or the car is asked to call 911 immediately.
Spokane police Capt. Dave Richards says the dead man's roommate was inside the home at the time of the shooting, but did not witness it.